Leaking drain under slab - crazy idea that I would like to run past everyone

Had a plumber come out to investigate why there was leakage and bad smells coming into basement from an interior cinderblock wall in my basement. It was discovered that the sink/dishwasher drain (cast iron) that spans the full length of the slab floor and through this cinderblock wall to the main sewer line in the basement was leaking. The leak flows more when water is run in the sink. I was told the best thing to do was to abandon this drain, cut the slab, and lay a new line. I was quoted $3400. Since I am about to start a total gut job kitchen remodel, this is an expense I am not prepared to have. I had planned on doing the work myself, but have a crazy idea that I would like to run past everyone. Along with the drain pipe there is a hot and cold supply as well as a 4" duct which provides heat to a register located in the toekick right below the sink cabinet.

My idea is to abandon the old drain pipe but instead of cutting the slab and replacing it I would like to abandon the use of the heat duct and simply run the new 2" drain pipe through the 4" duct. The second part of the question is should I do the same with the two water supply lines? The reason I ask is what happens if they have leaks as well or if not now then maybe at some point in the future. The problem I think I might have if I did run the new supply lines through as well is would I have noisy pipes since they would not be secured along this 12 foot span.

Are you sure it's the cast iron? It was common practice to use cast iron under the slab and continue through the roof with the vent and run a copper waste arm. ( horizontal line in wall to sink) It could the waste arm that has gone bad. This is a common repair in my area.

If you can install the pipe and have at least 3" of pitch on it, and secure so it stays that way, then it should work. There is no reason to assume the water lines will ever break, but if you are concerned install the water lines in the duct, but do not connect them at this time.

John,
That sounds plausable about the copper waste arm in the wall. I will have to see what it looks like when I remove the sink base. The reason I think it is the cast iron is because the water is leaking through the wall at the other end of the slab, 12' away from the sink where the cast iron exits into the basement. Is it possible for this water to make its way that far? I would think it would leech into the ground before it made it that far.

HJ,
Thanks for the response. I really don't want to have to break into the slab. I believe there is more than a 3" pitch because the place where the duct exits the wall is over 6" below the top of the slab.